The use of the three perpendicular theorem

1. The three perpendicular theorem describes the vertical relationship between PO (oblique line), AO (projection), and a (straight line).

2. a and PO can They may intersect or be in different planes.

3. The essence of the three-perpendicular theorem is the determination theorem that a diagonal line in space is perpendicular to a straight line in a plane. Regarding the application of the three-perpendicular theorem, the key is Find the perpendicular to the plane (datum plane). As for the projection, it is determined by the vertical foot and the oblique foot, so it is second. From the proof of the three perpendicular theorem, we get a procedure to prove a⊥b: one vertical , two projections, three proofs. That is, first, find the plane (datum plane) and the plane perpendicular. Second, find the projective line. At this time, a and b will become a straight line and an oblique line on the plane. Third, prove the projection. The line is perpendicular to straight line a, so a and b are perpendicular.

Note:

The four lines in the 1° theorem are all on the same plane

2 °The key to applying the theorem is to find the reference system of the datum.

Attachment: The "Teaching Requirements" of Jiangsu Province stipulates that from the 2011 college entrance examination, the "three perpendicular theorem" cannot be used as the basis for reasoning and argumentation and must be proved.

The "Teaching Requirements" of Heilongjiang Province stipulates that starting from the 2012 college entrance examination, the "Three Perpendicular Theorem" cannot be used as the basis for reasoning and argumentation and must be proved.